How Sensitive Are Sharks to Electric Fields?

Image: NOAA

It turns out that sharks (and some other fish) can detect electric fields. This sixth sense is called electroreception. I don’t know much about sharks (well, I think they’re cool), but I do know something about electric fields. According to Wikipedia, sharks can detect electric fields as small as 5 nV/cm or 5 x 10-7 V/m (volts per meter). Happy Shark Week or Shark Fest or whatever holiday it is (I get confused). Whatever week this is, my kids LOVE watching all the shark shows. Who could blame them?

Where is this going? Here is the problem. A show (can’t remember which) wanted to point out just how sensitive sharks are to electric fields. To demonstrate this, they had a diagram something like this:

Image based on screenshot from Google Maps

With an explanation something like this:

Suppose you put two D-cell batteries 1000 miles apart with a single wire connecting them. A shark could detect this faint voltage.

It was at this point I said “huh”? There seem to be a few problems with both the narrative and the diagram. Let’s talk about some physics first.

How Do You Make an Electric Field?

What is the electric field? Suppose I have two protons near each other. There is an electric force that pushes them apart, right? Now suppose I take away one of the charges so that there is just one proton. I can represent the possible electric interaction with an electric field. This is the force per unit charge due to the one proton in units of Newtons per Coulomb (where a coulomb is a unit of electric charge). I know that definition sort of sucks – you want something more real. But at this point, I think that’s the best I can give you. The electric field is this “thing” that surrounds electric charges.

And there is your answer. How do you make an electric field? Get an electric charge. If you want a larger electric field, get more electric charges. Now, be careful. If you get a billion protons and a billion electrons (which still isn’t very much matter), you would have electric fields that would add up. However, the net result would be a very small electric field since some the fields aren’t all in the same directions. This following diagram shows how we can represent the electric field for both positive and negative charges (the dotted line is there to indicate that these charges aren’t near each other).

You can find the magnitude of the electric field by finding the force on some known charge. If you take the force on this charge divided by its own value of charge, you get the electric field. This is commonly written as:

But what about this Volts per meter stuff? I guess you have to first look at the definition of a volt. Suppose I have some constant electric field with magnitude of E (don’t worry about how to make this field just yet). Now I want to move a proton with a charge of q a distance of s. If I am moving in the opposite direction as the electric field, this would require a force of Eq. Now I can calculate the work needed to move this charge.

Why am I even pushing this charge in a constant electric field? What is my motivation? Don’t worry about that. Worry about this instead – why if I want to change the charge and do it again? I could recalculate the work OR I could just write an expression for the work per unit charge by dividing both sides of the equation by the charge. This work per unit charge is essentially the same thing as the change in electric potential (also commonly called a voltage). The units for volts is a Joule per Coulomb.

In this constant electric field, I can write the change in potential in terms of the electric field and the distance:

Here you can see that the units for the electric field can also be described as a Volt per meter. Be very careful with the above expression. I made the assumption that the electric field had a constant magnitude. This isn’t always the case.

Oh, we were talking about sharks – right? Back to sharks.

What’s Wrong With the Example?

Ok, I think what they are trying to do is to show a really small electric field. But what about the two batteries? I’m not sure – but I can guess. Let’s try something. What if they used the above equation for electric field (change in electric potential divided by the distance)? One D-cell battery has a change in electric potential across the terminals of 1.5 volts. For the distance, I have 1,000 miles (1.6 x 106) m) – this gives:

Oh, am I a good guesser? You betcha. This electric field calculation of around 9 x 10-7 V/m is pretty darn close to the claimed minimum electric field of 5 x 10-7 V/m as stated on Wikipedia. So, I’m pretty sure that’s what they did.

Why is this wrong? Well, this start with the first thing. The above calculation assumes a constant electric field. How do you make a constant electric field? The most common way is with a parallel plate capacitor. If you get to plates near each other and connect one plate to one terminal of a battery and the other plate to the other terminal – you get a constant electric field.

But there is a catch. In order to get this constant electric field, you have to look near the center of these plates and the plates have to be close together relative to their size. If you want to put these plates 1000 miles apart, they would have to be HUGE in order to get a constant electric field.

What about the wire? Why is there a “single” wire connecting the two batteries? I really don’t know. Really, nothing would happen. There wouldn’t be an electric field inside the wire – if there were, there would be a current. Actually, this is something that is addressed in the Physics and Everyday Thinking curriculum (highly recommended for elementary education majors). In order to get current out of a battery, you have to have a complete circuit. Using the positive terminal from one battery and the negative from another just won’t work. Here are two circuits that show this.

This isn’t as clear as I had hoped. In case you can’t tell, the bottom setup has the lightbulb NOT on. You have to have a complete circuit for a battery to work. I’m still not sure why they have a wire in this explanation anyway.

Let me point out one more mistake. The narrative in the show says the shark could detect a faint voltage. From what I understand, sharks detect electric fields. Although the electric field can be measured in “volts per meter,” it is not a voltage. In order to measure a change in electric potential (the official name for voltage), you need to have two probes so that you can get a “change in” part of the electric potential.

Behind the Scenes

I have worked with productions like this before (in just an assisting role). Let me just imagine what happened. Our scene opens with two people. Producer enters stage left with the Science Advisor sitting at a computer.

Producer: We are working on some cool stuff for shark time. Did you know that sharks can detect voltages?

Science Advisor: I’m not too familiar with sharks, but Wikipedia says that they can detect electric fields, not voltage.

Producer: Great. Well, we need some type of statement that shows how sensitive sharks can be to these electric fields. What if we take a 1.5 volt battery. How far away would you have to be to get to field strength of 5 nV/cm? If I put this in my calculator, I get a distance of 1,800 miles. Let’s just call it 1,000 miles to make it simple.

Science Advisor: Actually, you did that wrong. You assumed that the electric field is constant outside of a battery. It isn’t.

Producer: Yes, but this gets across the idea that sharks are very sensitive to electric fields.

Both the producer and the science advisor are in tough positions. The producer wants to say something complicated in a very short and entertaining way. At the same time, the science advisor is trying to keep the stuff correct. It’s not as simple as it seems.

What Would I Do?

The goal is to find some example of a really small electric field. If you rub an inflated balloon on a sweater, it will acquire a net static electric charge. This charge will then create an electric field that we can calculate. But how much excess charge is on a balloon? It’s difficult to say – so let’s just make a basic estimate.

In the introductory physics textbook Matter and Interactions (great book), the authors estimate the excess charge on two tapes. If you haven’t done this before, it’s pretty cool. Take two pieces of clear tape that you would find in your desk and pull them apart. One tape will become positively charged and one will be negative. With some simple experiments, they estimate that a 20 cm piece of tape has about 10 nC (nano Coulombs) of excess charge on it. I don’t think it’s crazy to assume a rubbed balloon could have the same charge as this tape.

The nice thing about a balloon is that it’s spherically shaped. If the charge is uniformly distributed, then the electric field outside of the balloon will look just like the electric field due a point charge. Luckily, we have an expression for the magnitude of the field due to a point charge.

The stuff in the front is just a constant and the r is the distance from the center of the balloon. If the balloon as a charge of 10 nC, how far away could a shark detect it? I can solve the above expression for r and then put in the values for the minimum detectable electric field and the charge on a balloon. This gives a distance of 13 km or 8 miles. That seems crazy far. Well, as a check, the electric field on the surface of the balloon would be less than 3 x 106 V/m. This is the value of the breakdown strength of air. When the electric field is greater than this value, there will be a spark in the air. You can indeed get a balloon to make a tiny spark, so I guess that value isn’t so crazy.

Really, a shark wouldn’t likely be able to detect your charged electric balloon 8 miles away. I suspect this would fall under the background field strength from other stuff.

But the show must go on. I have to save the show. Here is the graphic I would make.

I put the distance at 4 miles for safety. If the shark could detect the balloon at 8 miles, then it could also detect it at 4 miles, right? I still think this is crazy, but at least it’s better than the 1000 mile long wire example. Oh, and for my example both the balloon and the shark are in a vacuum so that we can ignore the effects of the water.